## Midterm Information

### Updated 21 February

The Midterm Exam will be in class on Thursday, March 18th.

It will be a closed book, closed notes exam. Note that the Final Exam, which will include some more advanced material, will be open book, open notes.

There are two types of information intermixed here: The sections of the textbook you are responsible for as well as the types of questions you'll be responsible for in each section. Needless to say, the exam cannot cover every topic below. It will focus on approximately four of the eight topics below.

• Planes: (Chap. 2) Section 2.7.1 and 2.7.2. Be able to manipulate and compute from representations f(x,y,z) = ax + by + cz = 0, (p - a)⋅n = 0 and the related cross products that give the normal.
• Triangles: (Chap. 2) Be able to answer a question involving equations 2.29 through 2.31.
• Line drawing: (Chap. 3) I would give you the algorithm on pg. 58 and ask you to iterate it numerically for a few steps and explain why it's often more efficient than simply evaluating y = mx + b at each point.
• 2D transformations: (Chapter 5) You must be able to correctly write out and compute with 2D rotations and translations. You should get the order of multiplication straight and know that inverses can be simply decomposed so that if M = ABC, then M-1 = C-1B-1A-1.
• Shading: (Chap. 8) You should understand and memorize equation 8.2, and able to draw figure 8.1 and explain its relation to the equation. For the Phong lighting model, I may give you Fig. 8.5 and ask you to explain equation 8.5 qualitatively, using an eyepoint close to the reflected ray and one not as close. For this you need to understand the cosine function and how a high power of it behaves close to θ = 0. You should also be able to explain what Phong normal interpolation is used for - what artifact it avoids and how it avoids it.
• Ray tracing: (Chap. 9) In Sec. 9.3.1, you should be able to derive the equation that precedes the A, B, C form on page 155, starting with the simple equations for a ray and a sphere at the top of the page. Explain the significance of the double, single and imaginary roots for t in the resulting equation.
• Shadows: (Chap. 9). Be able to explain, along with carefully drawn diagrams corresponding to sections 9.5 and 9.11.2, how shadows and soft shadows are computed.
• Texture mapping: (Chap. 10) [details to be added after 2/26 class]